THE METAL-INSULATOR-TRANSITION - COMPLEXITY IN A SIMPLE SYSTEM

In 1949, Mott introduced a monatomic array of hydrogen atoms rigidly fixed to the sites of a cubic lattice as a model system with which to address the many-body physics of the metal-insulator transition. Hydrogen, in nature, does not conform to this model (the monatomic constraint is not met) but nevertheless hydrogen presents a system in which many of the major ideas post-dating Mott's paper are clearly manifested. The pairing of protons implies necessarily an even number of electrons per cell in crystalline phases, and hence the possibility of band-overlap metallization at sufficiently high density. However, the protons are highly quantum mechanical in their own right, and they possess non-trivial dynamics both translational and librational (and even rotational). On electronic timescales, the latter lead in the one-electron picture to a site-disorder problem and the possible emergence of localization phenomena. However, it is dynamic localization slaved to proton timescales, and a better view of the problem is one which treats electrons and protons on the same footing, a point of view that leads to the notion of pair localization and de-localization.